Question

HURRY PLEASE(NO LINKS)

Identify the polynomial that is the difference of two squares.

A. 36m^2 - 8n^8

B. 9m^2-5n^6

C. 25m^2 - 16n

D. 49m^2 - 81n^4

Answer 1

Difference of Squares

The difference of squares rule states that:

$a^2-b^2=(a+b)(a-b)$

A polynomial can only be a difference of two squares if a and b are both perfect squares.

Solving the Question

D. $49m^2 - 81n^4$

Out of all the given options, option D is the only polynomial in which a and b are both perfect squares. We know this because we can rewrite the expression as below:

$49m^2 - 81n^4\\= (7m)^2 - (9n^2)^2$

In this case, $a=7m$ and $b=9n^2$.

Answer

D. $49m^2 - 81n^4$